Problem 73 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used an exponential model with a positive growth rate to describe the depreciation in my car's value over four years.

Step-by-Step Solution

Answer

The statement doesn't make sense because an exponential growth model describes an increasing scenario over time, not a decreasing one like depreciation of a car's value.

Step 1: Understand the Characteristics of Exponential Models

An exponential growth model describes a situation that grows at a rate proportional to the amount present. Therefore, if the growth rate in this model is positive, the quantity increases. By nature of this model, the value being modeled cannot decrease over time.

Step 2: Analyze the Given Statement

The statement proposes using an exponential model with a positive growth rate to describe the depreciation of a car's value over four years. The depreciation of a car's value implies a decrease in value over time.

Step 3: Evaluate if the Model Fits the Situation

From the analysis, it's seen that an exponential growth model cannot correctly describe a scenario where the quantity decreases. Therefore, a positive growth exponential model would not accurately represent the depreciation of a car's value.